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arXiv · 2511.09670

Ladder Symmetry: The Necessary and Sufficient Condition for Vanishing Love Numbers

Chanchal Sharma·Shuvayu Roy·Sudipta Sarkar
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Abstract

Black holes in four-dimensional, asymptotically flat general relativity have vanishing static tidal Love numbers (TLNs), a property tied to a hidden symmetry of the perturbation equations. Within the Konoplya-Rezzolla-Zhidenko (KRZ) parametrization, a subclass of spacetimes was previously shown to admit such Ladder symmetry, which enforces the absence of static scalar TLNs. In this work, we introduce parametric deformations to such Ladder-symmetric spacetimes and analyze the resultant linear tidal response. Using the parametrized formalism for TLNs, we show that any deviation from a Ladder-symmetric background leads to non-zero static scalar TLNs. This establishes Ladder symmetry as a necessary, as well as sufficient condition, for the vanishing of static TLNs in static, spherically symmetric black holes and in rotating black holes of the KRZ class.

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Chanchal Sharma, Shuvayu Roy, Sudipta Sarkar. 2025-11-12. Ladder Symmetry: The Necessary and Sufficient Condition for Vanishing Love Numbers. https://doi.org/10.1103/44dg-smt2

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